Floating point numbers in Javascript

Initiate developers to the particularity of the floating point numbers implementation in javascript.

Transcript

1. Floating point numbers in javascript
2. Experiments “ Weird you will tell ”
3. Experiments $ node ! > 0.1 + 0.2 == 0.3 false ! > 0.1 + 0.2 == 0.30000000000000004 true ! > Math.pow(2, 1023) 8.98846567431158e+307 ! > Math.pow(2, 1024) Infinity ! > +Infinity + Infinity Infinity ! > -Infinity + Infinity NaN
4. Decimal representation • The every day used representation • The only one our brain can calculate in
5. Decimal representation • The every day used representation • The only one our brain can calculate in a = d[n]*10^n + d[n-1]*10^(n-1) + ... + d[0]*10^0 + ... + d[-p]*10^(-p)
6. Scientific Notation We’ve all seen numbers formatted like ! 6.02214129 * 10^23 Usually used in Physics. And this is the closest to the floating point representation we can get !
7. Floating point representation • Replicate the scientific notation • Use a binary format (for efficiency) • Maximize precision
8. IEEE 754 The representation of floating points in JavaScript follows the format as specified in IEEE-754. 6.02214129 * 10^23
9. IEEE 754 The representation of floating points in JavaScript follows the format as specified in IEEE-754. 6.02214129 * 10^23 • Sign on the first bit • Exponent encoded on 11 bits
 25 is the exponent in the exemple,
 because 2^78 < 6.022 * 10^23 < 2^79 • Significand encoded on 52 bits
 02214129 is the significand
10. IEEE 754 The representation of floating points in JavaScript follows the format as specified in IEEE-754. 6.02214129 * 10^23 • Sign on the first bit • Exponent encoded on 11 bits
 25 is the exponent in the exemple,
 because 2^78 < 6.022 * 10^23 < 2^79 • Significand encoded on 52 bits
 02214129 is the significand
11. Unit of Last Precision Number.prototype.exponent = function(){ return Math.floor(Math.log(this)/Math.log(2)); }; ! Number.prototype.bias = function() { return 1023; }; ! Number.prototype.biasExponent = function(){ return this.exponent() + this.bias(); }; ! Number.prototype.ulp = function(){ return Math.pow(2, this.biasExponent() - this.bias() - 52); }; Extends `Number` to compute the ULP.
12. Play ! http://bartaz.github.io/ieee754-visualization/
13. Compete with your pairs http://www.codewars.com/kata/526993d710342801b6000e85/train/javascript
14. Read more • http://blog.chewxy.com/2014/02/24/what-every- javascript-developer-should-know-about- floating-point-numbers/ • http://floating-point-gui.de/formats/binary/ • http://stackoverflow.com/questions/9383593/ extracting-the-exponent-and-mantissa-of-a- javascript-number